Vue component does propagate created data but not update/delete

Institute : Is a CRUD for the institute from the database and has Student's children

Student : is a CRUD for the student

MapBox : Create a OpenStreetMap

StudentMap : Is there to construct the layer with informations with leaflet

I retrieve from the database Institutes which have Students

I know I should need to use Vuex store to have a perfect and clean share of the datas but I had only one week to develop the project and I don't master Vuex still.

The Student component is responsible to edit/delete itself, Institute is responsible to create student, and edit/delete itself. The School, receive the Institutes via laravel json which bind it in the View at the loading.

Whenever an Institute or Student is created/update/deleted, I added event that emits from child to parent to update the data (which is the opposite of what Vue allow but in this usecase I need to let the master component (School) be up-to-date to propagate to the other branch MapBox -> StudentMap.

I have a watcher for the institute / student in the StudentMap and it is triggered when I add new Institute / Student. But when I update / delete, Nothing happen.